Nalepa graduated from the Music Academy in Rzeszów in the departments of violin, clarinet and contrabass. He received recognition in the category of duets at the 2nd annual "Festival of Young Talents" in Szczecin in 1963 along with Mira Kubasinska. They were married and had a son, named Piotr.

In 1965, Nalepa formed with Stan Borys band Blackout and started composing music to the lyrics of a poet, Bogdan Loebl. The Blackout's first concert was on September 3, 1965 in a club Łącznościowiec in Rzeszów. Tadeusz Nalepa recorded a self-titled album with Blackout along with six smaller recordings. The group disbanded in 1967.

In 1968, Nalepa formed a group called Breakout which existed for 13 years before disbanding in 1981. Breakout had released 10 albums. In 1982, he debuted as a solo artist in the Gwardia Hall in Warsaw in concert "Rock-Blok". The same year he recorded an album for Izabela Trojanowska as well as formed his own band which consisted of (besides Nalepa): Ryszard Olesinski (guitar), Andrzej Nowak (guitar), Bogdan Kowalewski (bass) and Marek Surzyn (drums).

On the May 25, 1985, Nalepa re-formed Breakout because of the band's 20th anniversary.

In 1986, magazine Jazz Forum named him the best musician, composer and guitar player. Along with the other winners, he took part in the concert series "Blues/Rock Top '86" and at the same time, he also started co-operating with another polish rock/blues band Dżem, (literally Jam). The two released a successful album Numero Uno.

After series of concerts abroad, Nalepa released a dual album, To mój blues (My Blues), which consisted recordings between 1982 and 1988.

In 1993, he performed with Nalepa-Breakout and the group released an album Jesteś w piekle (You are in Hell) and in the same year he was awarded the Maria Jurkowska Award by the III Program of the Polish Radio.

The following albums, as Tadeusz Nalepa, were released with different band members. His last release was a DVD 60 urodziny (60th birthday) (the only one in his catalogue), released in 2006 which contained a show from 22 November 2003. It was reissued later on as a DVD+Cd.